Summary

Testing the effect of deviance on similarity-based structure and certainty.

Hypothesis: We predict that as a new agent’s deviance from the group stereotype increases there will be a transition from group updating to subgroup formation to subtype formation. This will be reflected in participants’ similarity-rating derived dendrograms.

Method: 8 agents, 8 issues

Demographics (Attention Check)
0
(N=52)
0.25
(N=72)
0.5
(N=60)
0.75
(N=49)
1
(N=51)
Overall
(N=284)
age
Mean (SD) 35.4 (13.7) 36.1 (12.7) 33.9 (12.2) 37.7 (13.7) 36.9 (10.7) 35.9 (12.6)
Median [Min, Max] 32.0 [18.0, 72.0] 34.0 [18.0, 75.0] 33.0 [18.0, 71.0] 36.0 [20.0, 71.0] 35.0 [20.0, 62.0] 34.0 [18.0, 75.0]
race
American Indian or Alaska Native 1 (1.9%) 1 (1.4%) 2 (3.3%) 1 (2.0%) 0 (0%) 5 (1.8%)
Asian 6 (11.5%) 6 (8.3%) 8 (13.3%) 3 (6.1%) 6 (11.8%) 29 (10.2%)
Black or African-American 5 (9.6%) 5 (6.9%) 4 (6.7%) 6 (12.2%) 1 (2.0%) 21 (7.4%)
Hispanic/Latinx 3 (5.8%) 5 (6.9%) 5 (8.3%) 2 (4.1%) 1 (2.0%) 16 (5.6%)
White 37 (71.2%) 53 (73.6%) 41 (68.3%) 37 (75.5%) 41 (80.4%) 209 (73.6%)
Native Hawaiian or Other Pacific Islander 0 (0%) 1 (1.4%) 0 (0%) 0 (0%) 0 (0%) 1 (0.4%)
Other 0 (0%) 1 (1.4%) 0 (0%) 0 (0%) 2 (3.9%) 3 (1.1%)
gender
Man 20 (38.5%) 23 (31.9%) 19 (31.7%) 18 (36.7%) 24 (47.1%) 104 (36.6%)
Woman 32 (61.5%) 46 (63.9%) 40 (66.7%) 29 (59.2%) 23 (45.1%) 170 (59.9%)
Non-binary 0 (0%) 2 (2.8%) 1 (1.7%) 1 (2.0%) 2 (3.9%) 6 (2.1%)
Prefer not to answer 0 (0%) 1 (1.4%) 0 (0%) 1 (2.0%) 2 (3.9%) 4 (1.4%)
0
(N=4)
0.25
(N=6)
0.5
(N=2)
0.75
(N=2)
1
(N=3)
Overall
(N=17)
age
Mean (SD) 35.3 (9.46) 39.0 (21.8) 35.5 (4.95) 51.5 (21.9) 44.7 (26.3) 40.2 (17.7)
Median [Min, Max] 31.5 [29.0, 49.0] 29.5 [24.0, 82.0] 35.5 [32.0, 39.0] 51.5 [36.0, 67.0] 40.0 [21.0, 73.0] 34.0 [21.0, 82.0]
race
White 4 (100%) 5 (83.3%) 1 (50.0%) 2 (100%) 2 (66.7%) 14 (82.4%)
Asian 0 (0%) 1 (16.7%) 0 (0%) 0 (0%) 0 (0%) 1 (5.9%)
Black or African-American 0 (0%) 0 (0%) 1 (50.0%) 0 (0%) 1 (33.3%) 2 (11.8%)
gender
Man 1 (25.0%) 1 (16.7%) 1 (50.0%) 1 (50.0%) 1 (33.3%) 5 (29.4%)
Woman 3 (75.0%) 4 (66.7%) 1 (50.0%) 1 (50.0%) 2 (66.7%) 11 (64.7%)
Another gender not listed here 0 (0%) 1 (16.7%) 0 (0%) 0 (0%) 0 (0%) 1 (5.9%)
Agent Learning Plots
NonDeviant Analysis
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: corrresp
                                   Chisq Df Pr(>Chisq)    
opinion_round                   155.5722  1  < 2.2e-16 ***
Deviant_threshold                29.9063  4  5.114e-06 ***
opinion_round:Deviant_threshold   1.8352  4      0.766    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 1       opinion_round.trend     SE  df asymp.LCL asymp.UCL z.ratio p.value
 overall               0.186 0.0152 Inf     0.157     0.216  12.282  <.0001

Results are averaged over the levels of: Deviant_threshold 
Confidence level used: 0.95 
$emmeans
 Deviant_threshold emmean     SE  df asymp.LCL asymp.UCL z.ratio p.value
 0                   1.59 0.1099 Inf     1.374      1.80  14.461  <.0001
 0.25                1.04 0.0906 Inf     0.864      1.22  11.494  <.0001
 0.5                 1.01 0.0993 Inf     0.813      1.20  10.147  <.0001
 0.75                1.02 0.1099 Inf     0.807      1.24   9.303  <.0001
 1                   1.15 0.1080 Inf     0.943      1.37  10.692  <.0001

Results are given on the logit (not the response) scale. 
Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df asymp.LCL
 Deviant_threshold0 - Deviant_threshold0.25      0.5479 0.142 Inf    0.1611
 Deviant_threshold0 - Deviant_threshold0.5       0.5816 0.147 Inf    0.1795
 Deviant_threshold0 - Deviant_threshold0.75      0.5663 0.155 Inf    0.1440
 Deviant_threshold0 - Deviant_threshold1         0.4345 0.153 Inf    0.0161
 Deviant_threshold0.25 - Deviant_threshold0.5    0.0337 0.134 Inf   -0.3314
 Deviant_threshold0.25 - Deviant_threshold0.75   0.0185 0.142 Inf   -0.3688
 Deviant_threshold0.25 - Deviant_threshold1     -0.1134 0.140 Inf   -0.4964
 Deviant_threshold0.5 - Deviant_threshold0.75   -0.0153 0.148 Inf   -0.4180
 Deviant_threshold0.5 - Deviant_threshold1      -0.1471 0.146 Inf   -0.5457
 Deviant_threshold0.75 - Deviant_threshold1     -0.1318 0.154 Inf   -0.5508
 asymp.UCL z.ratio p.value
     0.935   3.864  0.0011
     0.984   3.945  0.0008
     0.989   3.658  0.0024
     0.853   2.832  0.0373
     0.399   0.252  0.9991
     0.406   0.130  0.9999
     0.270  -0.807  0.9284
     0.387  -0.103  1.0000
     0.252  -1.007  0.8525
     0.287  -0.858  0.9120

Results are given on the log odds ratio (not the response) scale. 
Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Similarity Plot
Similarity Analysis
Type III Analysis of Variance Table with Satterthwaite's method
                             Sum Sq Mean Sq NumDF DenDF  F value Pr(>F)    
targetpair                      334     334     1   284   1.6629 0.1983    
Deviant_threshold             33776   33776     1   284 168.2303 <2e-16 ***
targetpair:Deviant_threshold  45254   45254     1   284 225.3989 <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emtrends
 targetpair Deviant_threshold.trend   SE  df lower.CL upper.CL t.ratio p.value
 DN                        -62.2667 3.45 284   -69.05   -55.48 -18.057  <.0001
 NN                          0.0141 2.87 284    -5.63     5.66   0.005  0.9961

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 

$contrasts
 contrast estimate   SE  df lower.CL upper.CL t.ratio p.value
 DN - NN     -62.3 4.15 284    -70.4    -54.1 -15.013  <.0001

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 
ISM Plot
ISM Analysis
Analysis of Variance Table

Response: k
                   Df  Sum Sq Mean Sq F value    Pr(>F)    
Deviant_threshold   4  23.943  5.9857  16.327 4.967e-12 ***
Residuals         279 102.283  0.3666                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 Deviant_threshold emmean     SE  df lower.CL upper.CL t.ratio p.value
 0                   1.61 0.0840 279     1.44     1.78  19.178  <.0001
 0.25                1.66 0.0714 279     1.51     1.80  23.198  <.0001
 0.5                 1.87 0.0782 279     1.72     2.02  23.930  <.0001
 0.75                2.12 0.0865 279     1.95     2.29  24.471  <.0001
 1                   2.40 0.0848 279     2.24     2.57  28.348  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df lower.CL
 Deviant_threshold0 - Deviant_threshold0.25     -0.0451 0.110 279   -0.348
 Deviant_threshold0 - Deviant_threshold0.5      -0.2603 0.115 279   -0.575
 Deviant_threshold0 - Deviant_threshold0.75     -0.5064 0.121 279   -0.837
 Deviant_threshold0 - Deviant_threshold1        -0.7932 0.119 279   -1.121
 Deviant_threshold0.25 - Deviant_threshold0.5   -0.2152 0.106 279   -0.506
 Deviant_threshold0.25 - Deviant_threshold0.75  -0.4613 0.112 279   -0.769
 Deviant_threshold0.25 - Deviant_threshold1     -0.7481 0.111 279   -1.052
 Deviant_threshold0.5 - Deviant_threshold0.75   -0.2461 0.117 279   -0.566
 Deviant_threshold0.5 - Deviant_threshold1      -0.5329 0.115 279   -0.850
 Deviant_threshold0.75 - Deviant_threshold1     -0.2868 0.121 279   -0.619
 upper.CL t.ratio p.value
   0.2575  -0.409  0.9941
   0.0547  -2.269  0.1581
  -0.1754  -4.201  0.0003
  -0.4656  -6.647  <.0001
   0.0754  -2.033  0.2528
  -0.1534  -4.114  0.0005
  -0.4439  -6.751  <.0001
   0.0740  -2.111  0.2183
  -0.2163  -4.621  0.0001
   0.0458  -2.368  0.1273

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
 Deviant_threshold emmean     SE  df null t.ratio p.value
 0                   1.61 0.0840 279    2  -4.642  <.0001
 0.25                1.66 0.0714 279    2  -4.830  <.0001
 0.5                 1.87 0.0782 279    2  -1.656  0.0494
 0.75                2.12 0.0865 279    2   1.349  0.9108
 1                   2.40 0.0848 279    2   4.759  1.0000

P values are left-tailed 
New Agent Prediction Plot
Prediction Analysis
# A tibble: 2 × 8
  model    term          estimate std.error statistic p.value conf.low conf.high
  <chr>    <chr>            <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 below_.5 Deviant_thre…    -14.2      9.80     -1.45   0.149    -33.5      5.15
2 above_.5 Deviant_thre…    -14.3     10.6      -1.35   0.178    -35.2      6.59
Analysis of Variance Table

Response: confidence
           Df Sum Sq Mean Sq F value  Pr(>F)  
deviance    4   6957 1739.34  2.4753 0.04459 *
Residuals 279 196044  702.67                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 deviance emmean   SE  df lower.CL upper.CL t.ratio p.value
 0          60.3 3.68 279     53.1     67.6  16.411  <.0001
 0.25       56.1 3.12 279     50.0     62.3  17.961  <.0001
 0.5        53.2 3.42 279     46.5     59.9  15.546  <.0001
 0.75       48.4 3.79 279     40.9     55.8  12.778  <.0001
 1          46.1 3.71 279     38.8     53.4  12.419  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                    estimate   SE  df lower.CL upper.CL t.ratio
 deviance0 - deviance0.25        4.22 4.82 279   -9.030     17.5   0.874
 deviance0 - deviance0.5         7.13 5.02 279   -6.663     20.9   1.419
 deviance0 - deviance0.75       11.94 5.28 279   -2.552     26.4   2.262
 deviance0 - deviance1          14.23 5.22 279   -0.115     28.6   2.724
 deviance0.25 - deviance0.5      2.91 4.63 279   -9.811     15.6   0.628
 deviance0.25 - deviance0.75     7.72 4.91 279   -5.756     21.2   1.573
 deviance0.25 - deviance1       10.01 4.85 279   -3.308     23.3   2.064
 deviance0.5 - deviance0.75      4.81 5.10 279   -9.202     18.8   0.943
 deviance0.5 - deviance1         7.10 5.05 279   -6.760     21.0   1.407
 deviance0.75 - deviance1        2.29 5.30 279  -12.270     16.8   0.432
 p.value
  0.9063
  0.6159
  0.1604
  0.0530
  0.9704
  0.5158
  0.2388
  0.8799
  0.6239
  0.9927

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Moderator: Last Opinion
0
(N=52)
0.25
(N=72)
0.5
(N=60)
0.75
(N=49)
1
(N=51)
Overall
(N=284)
pred_maj
Yes 46 (88.5%) 56 (77.8%) 43 (71.7%) 41 (83.7%) 39 (76.5%) 225 (79.2%)
No 6 (11.5%) 16 (22.2%) 17 (28.3%) 8 (16.3%) 12 (23.5%) 59 (20.8%)
# A tibble: 4 × 9
# Groups:   pred_maj [2]
  pred_maj id      term  estimate std.error statistic p.value conf.low conf.high
  <lgl>    <chr>   <chr>    <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 FALSE    below_… Devi…   -12.7       24.5    -0.519   0.607    -62.3     36.9 
2 FALSE    above_… Devi…   -21.4       20.8    -1.03    0.312    -63.7     20.9 
3 TRUE     below_… Devi…    -8.26      10.5    -0.789   0.432    -29.0     12.4 
4 TRUE     above_… Devi…   -14.1       12.0    -1.18    0.242    -37.8      9.60
Analysis of Variance Table

Response: confidence
                   Df Sum Sq Mean Sq F value   Pr(>F)    
deviance            4   6957  1739.3  2.5929 0.036928 *  
pred_maj            1  10078 10077.5 15.0227 0.000133 ***
deviance:pred_maj   4   2162   540.5  0.8058 0.522346    
Residuals         274 183805   670.8                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Order of deviant across rounds
Opinion Round
0
(N=284)
1
(N=284)
2
(N=284)
3
(N=284)
4
(N=284)
5
(N=284)
6
(N=284)
7
(N=284)
Overall
(N=2272)
trialnum
0 45 (15.8%) 28 (9.9%) 41 (14.4%) 45 (15.8%) 39 (13.7%) 29 (10.2%) 32 (11.3%) 32 (11.3%) 291 (12.8%)
1 32 (11.3%) 31 (10.9%) 30 (10.6%) 43 (15.1%) 46 (16.2%) 46 (16.2%) 35 (12.3%) 43 (15.1%) 306 (13.5%)
2 39 (13.7%) 43 (15.1%) 42 (14.8%) 30 (10.6%) 39 (13.7%) 37 (13.0%) 40 (14.1%) 28 (9.9%) 298 (13.1%)
3 26 (9.2%) 34 (12.0%) 30 (10.6%) 33 (11.6%) 28 (9.9%) 37 (13.0%) 46 (16.2%) 36 (12.7%) 270 (11.9%)
4 31 (10.9%) 40 (14.1%) 32 (11.3%) 41 (14.4%) 33 (11.6%) 41 (14.4%) 32 (11.3%) 40 (14.1%) 290 (12.8%)
5 47 (16.5%) 31 (10.9%) 37 (13.0%) 31 (10.9%) 28 (9.9%) 29 (10.2%) 36 (12.7%) 22 (7.7%) 261 (11.5%)
6 32 (11.3%) 36 (12.7%) 37 (13.0%) 29 (10.2%) 35 (12.3%) 29 (10.2%) 30 (10.6%) 41 (14.4%) 269 (11.8%)
7 32 (11.3%) 41 (14.4%) 35 (12.3%) 32 (11.3%) 36 (12.7%) 36 (12.7%) 33 (11.6%) 42 (14.8%) 287 (12.6%)
Things to note

Possible interpretation of results:

Participants are demonstrating that they are learning about the deviant agent, but the degree of learning declines with subsequent tasks. This pattern could suggest that participant results reflect the first half of the structure learning model (up to the lowest point). Possible suggestion is to run 1B again with more chances to learn (ie more issues) to see if the results show an increase accuracy in learning about the deviant over a longer period of tasks.

Unresolved

-all good